You only need one copy of Nisus Writer, so trashing your old application won't cause your old documents to go missing or become unreadable. You generally want your copy of Nisus Writer to be located in your Applications folder. To make sure you have the latest version in that folder, select the application in the Finder and use the menu File > Get Info. The "Version" there should read 3.3.1.

If you somehow end up with two copies of Nisus Writer running and aren't sure where they are located, you can use the Dock's contextual menu (by right-clicking or Control-clicking the application icon in the Dock) and choosing the menu "Show in Finder".